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標題: 平面二桿撓性臂之解析動力學模式與控制設計
Analytical Dynamics Model and Control for a Planar Two-link Flexible Manipulator
作者: 潘建忠
Pan, Cheng-Chung
關鍵字: flexible manipulator;撓性臂;extended Hamilton''s principle;assumed modes method;延伸漢米爾頓原理;假設模態法
出版社: 機械工程學系
本論文先以延伸漢米爾頓原理(extended Hamilton’s principle),推導出無重力效應下平面二桿撓性機械臂之正確偏微分動力學方程式以及完整邊界條件。為了解析推導兩桿之模態函數和特徵頻率,本論文嘗試使用適當的撓性變形變數轉換以獲得齊次化的邊界條件。再利用假設模態法(assumed modes method)推導二桿撓性臂之常微分動態模式,並選取各桿的前兩個模態來展開,以求得供數值模擬用之近似模式。控制器設計方面,本文針對平面二桿撓性機械臂提出一結合回授線性化(以剛性模式為基礎)和LQR最佳化控制的複合控制策略,以LQR控制器補償回授線性化控制的不足,達成二桿機械臂之軌跡追蹤及主動式抑振的控制目標。

In this thesis, we first derived the exact partial differential equations and the complete boundary conditions for a planar two-link flexible manipulator by using the extended Hamilton's principle. In order to analyze the two links' mode shape functions and characteristic frequencies, we propose appropriate flexible-variable transformations to obtain homogenous boundary conditions in terms of new flexible variables. Then, dynamic ordinary differential equations for the two-link flexible manipulator are derived utilizing the assumed modes method, and by considering only the first two modes of each link, an approximate finite-dimensional model is obtained for numerical simulations.
In the controller design, we consider a composite control strategy consisting of the rigid model-based feedback linearization and optimal LQR controls to achieve both joint trajectory tracking and active vibration suppression of the two-link flexible manipulator. Computer simulations are presented for illustrating the effectiveness of the suggested control strategy.
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